Discrete & Computational Geometry

, Volume 33, Issue 2, pp 231–247 | Cite as

Cutting Triangular Cycles of Lines in Space

  • Boris AronovEmail author
  • Vladlen KoltunEmail author
  • Micha SharirEmail author


We show that n lines in 3-space can be cut into O(n2-1/69log16/69n) pieces, such that all depth cycles defined by triples of lines are eliminated. This partially resolves a long-standing open problem in computational geometry, motivated by hidden-surface removal in computer graphics.


Computational Mathematic Open Problem Computer Graphic Computational Geometry Depth Cycle 
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Copyright information

© Springer Science + Business Media Inc. 2004

Authors and Affiliations

  1. 1.Department of Computer and Information Science, Polytechnic University, Brooklyn, NY 11201-3840USA
  2. 2.Computer Science Division, University of California, Berkeley, CA 94720-1776USA
  3. 3.School of Computer Science, Tel Aviv University, Tel-Aviv 69978, Israel and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012USA

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